(1):

Find all irreducible polynomials of the form $\displaystyle x^2 + ax +b $, where a,b belong to the field $\displaystyle \mathbb{F}_3$ with 3 elements.

Show explicitly that $\displaystyle \mathbb{F}_3(x)/(x^2 + x + 2)$ is a field by computing its multiplicative monoid.

Identify [$\displaystyle \mathbb{F}_3(x)/(x^2 + x + 2)$]* as an abstract group.

any suggestions please?